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equal angles with midpoint of DC in trapezoid ABCD if AB = BD

Source: Sharygin Geometry Olympiad 2016 First Round P1 grade8

July 25, 2018
geometrytrapezoidmidpointequal angles

Problem Statement

A trapezoid ABCDABCD with bases ADAD and BCBC is such that AB=BDAB = BD. Let MM be the midpoint of DCDC. Prove that ∠MBC\angle MBC = ∠BCA\angle BCA.
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